In the radius of the anion in an ionic acid solid is 200pm, what would be the radius of the cation that fits exactly into a cubic hole:

Options

A. 146.4pm
B. 82.8pm
C. 45pm
D. none of these

Answer

To find the radius of the cation that fits exactly into a cubic hole formed by an anion in an ionic solid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The radius of the anion (R⁻) is given as 200 picometers (pm).
- We need to find the radius of the cation (R⁺) that fits into a cubic hole.

2. **Use the Radius Ratio for Cubic Holes**:
- The radius ratio (R⁺/R⁻) for a cation fitting into a cubic hole is approximately 0.732. This means:
\[ \frac{R^+}{R^-} = 0.732 \]

3. **Set Up the Equation**:
- We can express the radius of the cation (R⁺) in terms of the radius of the anion (R⁻):
\[ R^+ = 0.732 \times R^- \]

4. **Substitute the Value of R⁻**:
- Substitute the given radius of the anion into the equation:
\[ R^+ = 0.732 \times 200 \text{ pm} \]

5. **Calculate the Radius of the Cation**:
- Performing the multiplication:
\[ R^+ = 146.4 \text{ pm} \]

6. **Conclusion**:
- The radius of the cation that fits exactly into the cubic hole is **146.4 picometers**.

### Final Answer:
The radius of the cation is **146.4 pm**.